The authors describe a new gradient coil design for high resolution human, animal, specimen, or phantom imaging with high gradient efficiency and a large region of excellent gradient uniformity. Important features of our new design are the simple analytical description of the wire patterns that comprise the design, and ease of construction. Wires are spaced in a sinusoidal distribution around the circumference of the cylinder, and curved in an arcsin shape along the length of the cylinder. This coil produces a magnetic field pointing in a direction transverse to the axis of the coil with a gradient in the direction parallel to the axis of the coil. The same arcsin coil can be used to create a magnetic field pointing in a direction parallel to its axis with a gradient in a direction perpendicular to the coil axis. A prototype coil was constructed; field and inductance calculations were verified. Geometric variations on this coil design were modeled and their performance characteristics compared. This coil design is ideal for rapid implementation of a transverse gradient coil, since no specialized design software is required.